Service Battery warning but diagnostics give me ADP000 - No issues

169 cycles on a battery that's perhaps six years old suggests it has been used somewhat less than optimally. More recent Macs and operating systems subsequent to Mojave (what you're using) incorporate optimization features designed to maximize their useful life: About battery health management in Mac laptops - Apple Support. Prior to that, we had to remember to exercise batteries on our own.

I'd get that battery replaced. It's not cost-prohibitive, and will extend your Mac's useful life so that you can continue to use your old scanner. Start here: Get help with your Mac laptop battery - Apple Support, which directs you to contact Apple.

OUCH! Let's not do this anymore:

I let the battery run down to 0 percent, let it set for a day, charging it back up to 100%, same errors.

So-called battery sites in the internet paint with an overly-broad brush and forget to tell readers that Apple stopped recommending that (it's "calibration") about 2009 —14 years ago!

I have always held the belief that, unless your have widely-known issues (Mojave does not), you address the service issue BEFORE upgrading. Jumping to an upgrade can make the problems worse. Your call.

Is this the original Apple battery?

Is the runtime between charging acceptable?

The warning is just that ... a warning. It doesn't detect anything broken. It's set to prompt when you get to a certain value on remaining capacity. For an MBP that's 80%

You don't have to heed the warning, but your Macs performance will begin to suffer. You need to have a fully capable battery.